Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons
Soroush Vahidi, Ioannis Koutis
TL;DR
The paper reframes ranking from pairwise comparisons as a Minimum Weighted Feedback Arc Set problem, enabling a simple, learning-free framework that removes minimal-weight cycles to yield a DAG and a consistent ranking via topological sort. It adopts a local-ratio heuristic for efficiency, demonstrates fast runtimes and competitive accuracy on benchmark datasets, and introduces weighted and margin-based loss formulations to evaluate rankings under edge weights. A post-processing step reduces ratio upset loss without affecting the ranking order, further improving evaluation without altering rankings. Overall, the work shows that lightweight combinatorial techniques can scale to large ranking tasks with practical performance comparable to learning-based approaches, while offering modularity to balance speed and quality.
Abstract
The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using learning based methods, but did not examine the underlying connection to MWFAS. In this paper, we investigate this relationship and introduce efficient combinatorial algorithms for solving MWFAS as a means of addressing the ranking problem. Our experimental results show that these simple, learning free methods achieve substantially faster runtimes than recent learning based approaches, while also delivering competitive, and in many cases superior, ranking accuracy. These findings suggest that lightweight combinatorial techniques offer a scalable and effective alternative to deep learning for large scale ranking tasks.